A273399 a(n) = Catalan(Catalan(n)).

1, 1, 2, 42, 2674440, 39044429911904443959240, 10934377152170553993439479038404269881062854488806451985760537780703486068308

Offset

0,3

Comments

Next term, a(7), which has 255 digits and is equal to Catalan(429), is too large to include.

The number of digits of a(n) grows faster than Fibonacci(n) or Catalan(n-1), but slower than Catalan(n).

Links

Amiram Eldar, Table of n, a(n) for n = 0..8

Formula

a(n) = A000108(A000108(n)).

Example

a(3) = Catalan(Catalan(3)) = Catalan(5) = 42.

Maple

a:= ((n-> binomial(2*n, n)/(n+1))@@2):
seq(a(n), n=0..7);  # Alois P. Heinz, Jun 12 2016

Mathematica

CatalanNumber[CatalanNumber[Range[0, 6]]]
Table[CatalanNumber[CatalanNumber[n]], {n, 0, 6}]

Prog

(PARI) a(n) = my(cn = binomial(2*n, n)/(n+1)); binomial(2*cn, cn)/(cn+1);

Crossrefs

Cf. A000108 (Catalan), A273400 (related sequence).

Sequence in context: A330229 A039622 A130506 * A052078 A069544 A256285

Adjacent sequences: A273396 A273397 A273398 * A273400 A273401 A273402

Keyword

nonn,easy

Author

Waldemar Puszkarz, May 21 2016

Status

approved